uncoupled pressure solutions
 

hey

can anybody explain in simple words that wht is the meaning of uncoupled pressure solutions and why in staggered grid uncoupled pressure solutions are not obtained..

thanks

See the book of Patankar - Numerical Heat transfer and Fluid Flow.

basically the staggering of the mesh allows one to calculate the pressure field such that the continuity equation is also satisfied. by not creating a staggered grid...the pressure field would be uniform and hence the pressure drop across the region under consideration zero....thereby negating the influence the effect of pressure on the flow.

the other way avoid staggered grids is to use the momentum interpolation...that allows on to place the velocity and the pressure nodes on the point...

refer to patankar or versteeg for staggered grids and schafer for collacted grids the latter option

When the grid is not staggered, the classical discretization of the pressure equation is such that adjacent nodes will be decoupled (i.e., in the equation for the node i,j will not be present the pressure at nodes i/j +/-1 but at nodes i/j +/-2). As a consequence, up to 4 different values of the pressure can be present even where the pressure should be constant. This, in turn, can destabilize the solution.

In practice this means that the laplacian discretized in this way is not responsive to perturbations which act at the Nyquist cut off frequency, i.e., they are not damped, and this is clearly not physical.

Several ways exist to handle this situation; one of these is the momentum interpolation which is just the addition of an additional diffusive-like term (discretized differently) which damps the obscillations (the most popular method); a second one is to just discretize the pressure term in its final form which is equal to admit a second order error in the mass conservation equation (this should be avoided). The adoption of a staggered grid does not need anything because the pressure discretization on this kind of grids does not suffers this issue; however this is not practical for unstructured grids and is seldom adopted. An additional method is to apply certain kind of filters to the decoupled solution which should remove the obscillations.